Contributions of Oxygen Dissociation and Convection to the Behavior of a Compartmental Oxygen Transport Model

A Compartmental Model for Oxygen Transport in Brain Microcirculation in the Presence of Blood Substitutes

“…The venous and tissue PO 2 are reduced with an increase in consumption rate. The tissue PO 2 is lower than the venous PO 2 when the consumption rate is elevated by 50% from the control whereas it becomes higher than the venous PO 2 when the metabolic rate is reduced by 50% for both values of P 50p : The prediction of tissue PO 2 lower/ higher than the venous PO 2 is consistent with the earlier studies (Ye et al, 1993(Ye et al, , 1994Sharan et al, 1998b).…”

“…Ye et al (1992) have described an averaging procedure to derive equations from the spatially distributed to a compartment model. Using this procedure, Ye and his coworkers have also proposed a compartmental M. SHARAN AND A. S. POPEL model in the microcirculation, similar to ours, for oxygen transport (Ye et al, 1993) and combined oxygen and carbon dioxide transport (Ye et al, 1994(Ye et al, , 1998.…”

“…At the moment, it is not clear how to derive these in terms of flow-averaged variables. Ye et al (1992Ye et al ( , 1993 have derived the compartmental equation for the homogeneous blood by considering the crosssectional averages which are in general valid for a uniform flow. Also, they have pointed out the discrepancy in evaluation of cross-sectional average of fractional saturation in terms of cross-sectional average of partial pressure.…”

Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

“…In the present work, we choose γ = 2, which corresponds to a parabolic velocity profile of a Newtonian fluid. This is in agreement with the results of in vivo velocity measurements made by Doppler optical coherence tomography (Kassab et al 1997;Song et al 2014) and with the modeling assumptions in Sharan and Popel (2002) and Ye et al (1994Ye et al ( , 1993. Following the procedure detailed in Formaggia et al (2009), we obtain from system (1) the following two-phase version of the classical Hagen-Poiseuille model in the variables Q b = Av s , volumetric flow rate, H D , hematocrit, and p b , pressure:…”

“…1: (1) a model for the retinal microcirculation, consisting in a vascular tree network (VTN) formed by arterioles, venules and capillaries organized in a graph. Blood flowing in the VTN is modeled as a two-constituent mixture of Newtonian incompressible fluids, plasma and red blood cells (RBCs) (Ye et al 1993;Sharan and Popel 2002;Liu et al 2009). Oxygen is transported by blood and filters out from the vessel walls into the surrounding tissue, where the amount of permeating solute depends on the tissue metabolic demand (Popel 1989).…”